5GNSS: Fusion of 5G-NR and GNSS Localization for Enhanced Positioning Accuracy and Reliability

With the proliferation of connected devices and the increasing demand for more precise and reliable positioning information, the fusion of 5G and GNSS localization systems holds immense potential to overcome the current limitations of standalone approaches. In order to tackle this challenge, in this paper we explore the potential of the fusion of 5G-NR and satellite localization systems to jointly enhance their accuracy and reliability. The designed solution, termed 5GNSS, is explained in detail, describing its five main building blocks and corresponding mathematical foundations. An extensive performance evaluation has been conducted, considering urban, suburban, and rural vehicular scenarios, as well as a varying number of visible satellites and 5G base stations. Our results show that 5GNSS can outperform standalone GNSS, 4G-LTE and 5G-NR positioning systems consistently across all these scenarios with an average error reduction in the $\sim$ 60-40% range. Based on these results, we conclude that future positioning systems would strongly benefit from incorporating 5GNSS-like fusion solutions.


5GNSS: Fusion of 5G-NR and GNSS Localization for Enhanced Positioning Accuracy and Reliability
Federico Campolo , Andra Blaga , Maurizio Rea , Angel Lozano , Fellow, IEEE, and Xavier Costa-Pérez , Senior Member, IEEE Abstract-With the proliferation of connected devices and the increasing demand for more precise and reliable positioning information, the fusion of 5G and GNSS localization systems holds immense potential to overcome the current limitations of standalone approaches.In order to tackle this challenge, in this paper we explore the potential of the fusion of 5G-NR and satellite localization systems to jointly enhance their accuracy and reliability.The designed solution, termed 5GNSS, is explained in detail, describing its five main building blocks and corresponding mathematical foundations.An extensive performance evaluation has been conducted, considering urban, suburban, and rural vehicular scenarios, as well as a varying number of visible satellites and 5G base stations.Our results show that 5GNSS can outperform standalone GNSS, 4G-LTE and 5G-NR positioning systems consistently across all these scenarios with an average error reduction in the ∼ 60-40% range.Based on these results, we conclude that future positioning systems would strongly benefit from incorporating 5GNSS-like fusion solutions.

I. INTRODUCTION
T O DATE, most location-based services have largely relied on global navigation satellite systems (GNSSs) to retrieve positioning information.To estimate the position of a user equipment (UE), a GNSS applies the principle of multilateration, exploiting the ranging information from different satellites.However, ionospheric and tropospheric effects, multipath, clock errors, as well as the loss of satellite visibility strongly affect the GNSS-only positioning error.As a result, GNSS positioning is limited to a meter-level accuracy [1].
With the advent of advanced localization use cases such as smart cities, public safety systems, smart factories, and autonomous robotics, more stringent requirements are defined that render GNSS-only accuracy insufficient.In this context, one sector stands out: intelligent mobility.Indeed, road accidents, congestion, and pollution pose significant challenges to modern cities, and autonomous vehicles present an opportunity to address these issues [2].However, new and more accurate positioning systems are needed to make it possible.
As per the latest standardization efforts of the society of automotive engineers (SAE), driving automation ranges from level 0 (no automation) to level 5 (full automation) [3].Across these levels of automation, vehicles can undertake intelligent operations such as collision avoidance, lane departure warning, traffic sign detection, and contribute to traffic flow management and congestion reduction [4].However, a continuous and highly precise estimation of the vehicle's position is vital for the correct functioning of autonomous driving, as highlighted by the SAE standard and ETSI guidelines [5], and these requirements cannot be met by GNSS alone.
To tackle this challenge, the extensive coverage provided by cellular networks becomes valuable.While early cellular standards enabled only coarse precision (say cell-level accuracy [6]), newer generations, notably 5G-NR, have significantly elevated the potential accuracy.Specifically, higher temporal resolutions and larger arrays of antennas allow for more precise estimations of a signal's time of flight (ToF) and direction of arrival [7].
This paper explores the potential of 5G-NR to improve the performance of GNSS-only positioning.In particular, a fusion localization solution termed 5GNSS is proposed that jointly considers the ranging measurements from both 5G-NR and GNSS to outperform both stand-alone systems.While the focus is on vehicular scenarios, the benefits of more accurate and robust positioning is expected to extend into other disruptive applications yet to be envisioned.The main contributions of the paper can be summarized as follows: r Definition of a novel approach for the fusion of 5G-NR and GNSS, in a flexible framework allowing for potential future inclusion of other inputs.The design facilitates an easy and wide commercial adoption through the integration of largely available technologies and the possibility of retrofitting.
The remainder of the manuscript is structured as follows.Section II reviews related work and established the state of the art.Then, the basic theoretical principles behind positioning by multilateration, GNSS pseudoranges, and 5G-NR ToF measurements are presented in Sections III, IV, and V, respectively.The exposition continues with the introduction of 5GNSS in Section VI and a thorough description of the simulation framework in Section VII.Next, Section VIII exemplifies the performance in urban, suburban, and rural scenarios.Finally, Section IX concludes the paper and outlines potential follow-up research.

II. RELATED WORK
State-of-the-art positioning solutions rely on different approaches to alleviate the performance degradation of GNSS in certain scenarios; these combine GNSS measurements with those of cellular networks, inertial sensors, or other types of sensors.This section reviews the most relevant solutions proposed to date and highlights their differences with 5GNSS.
The potential of 4G-LTE in providing a localization solution, either alone or in conjunction with GNSS, is assessed in [8], [9], [10], [11], [12].These works consider the time-difference-ofarrival and the roundtrip time and, for the fusion with GNSS, they investigate the use of Kalman and other filtering approaches.As in our case, all proposals obtain ranging estimates through the observation of a received reference signal.The present paper considers 5G-NR in lieu of LTE, with the benefit of a higher temporal resolution.
The hybridization of GNSS with 5G-NR has also been studied [13] in works that can be roughly classified into three categories: theoretical studies [14], [15], point positioning methods [16], [17], and temporal-filtering-based methods [13], [18].In contrast, 5GNSS avoids the complexity of filtering-based methods (e.g., an extended Kalman Filter) while taking advantage of the different sample rates of the two systems, relying only on standard signal processing techniques.
The fusion of GNSS with information from inertial sensors, inertial measurement units, and 3D digital maps is investigated in [19], [20], [21], [22], [23], [24].Differing from these approaches, 5GNSS does not rely on sensor information or complex maps, which might not be available.However, such resources, if available, might complement 5GNSS to further improve its accuracy.
A computer-vision-based approach exploiting single or stereo cameras, together with inertial sensors is proposed in [25], [26], [27].While this is an interesting approach in terms of accuracy, it faces challenges in difficult atmospheric conditions or at night.Being robust in poor lighting and/or atmospheric conditions, 5GNSS is complementary to such systems.
Finally, the use of RADAR and LiDAR sensors within the autonomous driving scope is investigated in [28], [29], [30], [31].While these approaches exhibit strong performance and robustness to varying environmental conditions, they rely on equipment that is very costly and not readily available in every vehicle.Instead, 5GNSS, relies on equipment expected to be widely deployed (GNSS and 5G) and is potentially retrofittable, making it available to the assisted/automated driving mass market at a large scale as well as to other potential applications.

III. POSITIONING BY MULTILATERATION
In most positioning systems, including GNSS, location information is retrieved by performing multilateration.With a view to positioning in 2D space, a 2D map is considered where p n = (x n , y n ), n = 1, . . ., N, are the known positions of a set of N nodes.The objective is to estimate the unknown position p = (x, y) of a UE.The distance-or range, the two terms are used interchangeably in the sequel-between the UE and the nth node is [9] with c the speed of light, τ n the ToF, and • the Euclidean distance.Positioning applications refer to a system time and, as the UE and nodes clocks are generally not perfectly synchronized with this system time, the measured distances are affected by an unknown bias in addition to the inevitable errors caused by noise.Assuming that node synchronization errors are known and can be compensated, once at least four distance measurements dn are collected, the UE can apply multilateration to estimate both its location and its own clock error, namely [32] δt with d and d the vectors of real and estimated distances between the N nodes and the UE, respectively, and δt UE the UE clock error.
Each of the N distance estimations, centered at the corresponding node, defines a circle of radius dn .Because of the errors induced by noise, and additional distortions in the estimations, these circles do not intersect at a point, but rather define an area.To solve (3), nonlinear least-squares (NLLS) estimation can be applied.NLLS estimation linearizes the quadratic form through a Taylor expansion, rearranging the gradient equations of the problem into a set of linear equations.To solve these equations, an iterative procedure such as the Gauss-Newton algorithm is employed [33].
The efficacy of multilateration is closely tied to the quantity, quality, and geometry of the measurements.This dependency on measurements characteristics is captured by the horizontal dilution of precision (HDOP), which indicates the extent to which errors in distance estimation and the arrangement of nodes impact the accuracy of position estimation on the horizontal plane [34].

IV. GNSS PSEUDORANGE ESTIMATION
GNSS is a collective term for systems providing a UE with a positioning solution from signals emitted by orbiting satellites.Various such systems guarantee global coverage, chief among them the NAVSTAR global positioning system (GPS).A GNSS comprises a constellation of satellites, and their visibility to the UE is influenced by signal blockage.Consequently, only a subset of J satellites is observable from the UE.Signal blockage depends on the elevation mask at the UE, which defines the minimum elevation angle at which satellites are visible.Specifically, the elevation of satellites is defined as the angle between the tangent to the Earth curvature and the line-of-sight (LoS) to the satellite and the elevation mask is determined by the ratio between building height and street width.The impact of signal blockage is more pronounced for low-elevation satellites and becomes even stronger in dense urban areas where the presence of tall buildings shrinks the elevation mask.
Each satellite broadcasts a signal containing a ranging code and a data message; the code indicates the transmission time of the signal while the message includes parameters and information about the satellite's orbit.From these signals, the UE computes a position and time solution at a rate R GNSS , up to 10 Hz.Positioning is performed via multilateration, based on the distance from the UE to each visible satellite, estimated from the ToF of the J received signals.
If the UE and satellite clocks were synchronized, the range ρ j from the jth satellite to the UE would satisfy ρ j = τ j c [32].However, as mentioned, UE and satellites clocks are not synchronized, and the atmosphere slightly perturbs the speed and direction of the propagation.The measured distance is hence afflicted by a bias, in addition to the noise-induced errors, and the ranging estimate ρj is aptly termed pseudorange.Specifically, the bias introduced by the lack of synchronization is δρ j = (δt UE − δt j )c, with δt j the clock error with respect to system time of the jth satellite [32].
Satellite clock errors are measured and transmitted in the data message, allowing for their correction at the UE.Conversely, δt UE is unknown and therefore treated as additional parameter to be determined.The pseudorange measured at the UE after correcting the satellite clock errors equals [32] Subsequently, the UE speed can be obtained from the rate of change of the pseudorange.

V. 5G-NR TOF ESTIMATION
The 5G-NR standard features a variety of reference signals [35]; these can be dynamically allocated within each slot, thus adapting their sample rate R 5G-NR .Any of them is, in principle, suitable for localization purposes, chiefly the positioning reference signal (PRS).However, their performance for this purpose is hampered by two issues: hearability and resource element density.The former limits the number of nodes (gNBs in 3GPP parlance) that a UE can hear simultaneously through the same reference signal, while the latter reduces the bandwidth of the reference signal, which in turn constraints the accuracy of range estimations.To address these limitations, 3GPP Release 16 introduced a new version of the PRS, which we dwell on in Section VII-B.
The ToF can be inferred through a maximum likelihood (ML) procedure, searching for the peak of the circular crosscorrelation between the transmitted and received reference signals [8], [36].Generally constructed from a sequence of the constant amplitude zero autocorrelation (CAZAC) family, reference signals exhibit the zero autocorrelation property with ξ being the considered sequence, ξ its complex conjugate, N the length of the sequence, and q the delay.
Letting u and v be the transmit and received reference signals, with U and V their frequency-domain counterparts, the circular correlation satisfies As a result, the estimated ToF can be found from the largest peak of the circular cross-correlation as and the distance between the th gNB and the UE then follows as d = τ c.The above procedure entails considerable complexity and requires the complete knowledge of the signal, which is an issue when the reference signal is interspersed with payload data.An example on how to approximate efficiently the above ML solution through an estimator (e.g., a Fitz Estimator) can be found in [37].
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VI. 5GNSS DESIGN
This section sets forth the concept and principles underlying 5GNSS, which, through the fusion of distance measurements from both 5G-NR and GNSS, surpasses the capabilities of standalone systems.A detailed description of the key components of 5GNSS, illustrated in Fig. 1, is then provided in the subsequent sections.As described in Sections IV and V, GNSS and 5G-NR produce respective distance estimations at rates R GNSS and R 5G-NR .In general, R 5G-NR > R GNSS , hence 5G-NR produces F = R 5G-NR /R GNSS as many samples.Over one GNSS interval, hence in between two subsequent samples of GNSS, the 5G-NR measurements collected from the L gNBs can be assembled into the matrix As mentioned in Section III, the precision of distance measurements significantly influences the efficacy of multilateration, and this impact can be quantified through the HDOP.This is leveraged, through a series of standard yet effective processing steps over the samples window, to enhance the final positioning accuracy.

A. Measurement Preprocessing
The first step of the processing pipeline consists on cleaning the matrix of samples D from outliers and noisy measurements.In particular, 5G-NR samples are affected by noise, multipath and other non-line-of-sight (NLoS) effects.By analyzing the variance of the measurements, and by taking into consideration the signal-to-noise ratio (SNR) at the receiver, the preprocessing block can filter these estimates to avoid large errors in the positioning process.Specifically: r Outliers are removed.For the sake of specificity, we declare as outliers the distance estimates that are more than three scaled median absolute deviations away from the median for each gNB.With that, the measurement preprocessing block returns a matrix D of filtered measurements (see Fig. 2).

B. Oversampling and Smoothing
Due to the removal of overly noisy measurements and outliers, within a GNSS interval not every gNBs produces exactly F measurements.For this reason, this block expands the amount of samples through oversampling and subsequently applies an exponential weighted moving average (EWMA) for smoothing.
Denoting by a the oversampling factor, the block linearly interpolates the distance estimates of each gNB within the GNSS interval.As a result, each gNB will now have aF distance measurements d (1) , . . ., d (aF ) .
The system then applies an EWMA to smooth the measurements, which helps to increase the accuracy as will be seen in Section VIII.Specifically, with n = 1, . . ., aF and with β set according to the UE speed, ν, following a model that is determined a-priori through a speed analysis.In this analysis, the value of β that minimizes the root mean-squared error (RMSE) of 5G-NR distance measurements is found for ν ∈ [10, 300] km/h.As depicted in Fig. 2, the block

C. Rate Matching
To attain the fusion leading to a position solution at R GNSS , synchronization between both systems is imperative.Drawing from findings in prior studies [14], [16], we make the that the 5G-NR network maintains synchronization with the GNSS satellites.It is worth noting that a two-way protocol might offer a potential avenue for reducing synchronization errors [38].However, it is important to clarify that a comprehensive analysis of such a protocol is beyond the intended scope of this paper.To equalize the rates, the matching block takes as input the matrix of cleaned and corrected measurements D and, for each available gNB, it selects only the last of the aF samples.

D. Fusion Measurement Stacking
Once samples at rate R GNSS are available for both systems, the stacking block fuses them.One or more predefined parameters determine L weights w gNB for the gNBs and J weights w Sat j for the GNSS satellites.These weights enable assigning greater significance to the system, 5G-NR or GNSS, exhibiting superior performance, while still benefiting from additional information.In Section VII-C, we elaborate on the process of selecting these parameters to define a set of weights and on how these weights can can yield to a more accurate outcome in the multilateration process for our evaluation framework.
The weighted measurements are stacked into the vector   (11) and is solved via NLLS using the Gauss-Newton method with line-search for the step size.This is initialized with the linear least-squares solution found using only the subset of ζ corresponding to 5G-NR measurements, whose latency is lower than that of GNSS.The location estimator returns a vector of 2D coordinates in the chosen reference system.

VII. EVALUATION FRAMEWORK
This section describes the framework used for the evaluation of 5GNSS.Three distinct scenarios are considered.
r Rural: characterized by the complete absence of obstacles for both 5G-NR and GNSS signals, hence the channels are LoS.The UE moves at an average speed of 56 km/h.r Suburban: low-density urban environment where buildings are generally short, reducing somewhat the visibility between the UE and gNBs/satellites.The average UE speed is 30 km/h.r Urban: the harshest of the three environments, featuring a density of high-rise buildings and so-called urban canyons.This environment exhibits strong multipath and severely reduced visibility between the UE and the satellites.The average UE speed is 36 km/h.These scenarios are supported by actual GNSS trajectories collected in [39].This dataset contains 40 hours (corresponding to 1300 km) of data extracted through the CAN BUS of a vehicle, as well as 58 hours (corresponding to 4400 km) of smartphonerecorded data, all sampled at 10 Hz.The portions of dataset used as ground truth for the scenarios include the tracks shown in Fig. 3, recorded in and around the town of Coventry, U.K.Besides the UE latitude and longitude coordinates, also its speed, heading, number of visible satellites at each sampling instant, and time, are all extracted.
The gNBs, in turn, are placed on positions within the considered geographical areas that are extracted from Cellmapper, 1 an online map-based dataset providing information about the gNBs of operators in a variety of countries.As the exact latitude, longitude, and altitude of the gNBs is not provided, we rely on Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the map supplied by the website alongside Google Maps 2 to manually collect these coordinates.Finally, to recreate the 3D environments of the urban and suburban scenarios, the 3D maps available at OpenStreetMap 3 are utilized.

A. GNSS Simulation Environment
GNSS is simulated by means of the Aerospace toolbox, together with the RINEX files of GPS and Galileo constellations available in Matlab 2022b. 4These allow re-creating the configuration and movements of the entire constellations of GPS and Galileo during a specific time interval.Once the geographical area is specified, the toolbox also allows determining how many satellites are visible and simulates the reception of navigation messages from each.As explained in Section IV, these messages are used by the UE for ranging and subsequent multilateration.The time interval of the dataset is considered, where R GNSS = 10 Hz.
To simulate the visibility of satellites, the model presented in [16] is invoked.It entails defining an elevation mask θ j for the jth satellite, which depends on its azimuth angle φ j as well as on the width of the street x d and the height of the buildings z h via where with θ max the maximum elevation mask at φ j = 0.The values are set to θ max = 0 in the rural scenario, θ max = 30 • in the suburban scenario, and θ max = 60 • in the urban scenario.This choice is justified next.Validation: Fig. 4 compares the number of simulated visible satellites against the ones seen from an actual UE in a similar scenario.To do so, the GnssLogger App on an Android UE is used, which allows collecting raw information on the visible satellites.Generally, a UE can receive signals from a variety of constellations, but for a fair comparison only the visible Galileo and GPS satellites (the ones being simulated) are considered.The three scenarios are recreated while travelling on a vehicle between the cities of Barcelona and Lleida, collecting all the necessary information about the two constellations.In particular, the urban scenario is recreated considering the data collected within the two cities themselves, the suburban corresponds to the data collected in the areas right outside, and the rural to the data collected in an open rural area in-between.To render the results comparable, Matlab is set to the date/time as well as the geographical coordinates of this trajectory, and the RINEX files of the constellations are used, collected by the UE through the App.As can be seen in Fig. 4, the number of satellites visible from the real UE (blue line) is highly variable, while the simulator presents a fixed number of visible satellites.However, this fixed number does approximate rather tightly the average number of visible satellites in all three scenarios, and always in a conservative fashion.To gauge how the difference affects the performance, a sensitivity analysis is conducted whereby the RMSE of 5GNSS is evaluated for a varying number of gNBs and visible satellites, in an ad-hoc scenario.Fig. 5 depicts the results by means of a heat map.The error decreases quickly as the total number of nodes used for positioning increases.Specifically, fixing the number of gNBs to two, having 8 satellites vs 11 causes only a very small change in RMSE.The same can be said for 15 satellites vs 18.This difference becomes even less relevant as the number of available gNBs increases.

B. 5G-NR Simulation Environment
Each gNB features three sectors centered at 0, 120, and 240 degrees, each of them equipped with a 3GPP-compliant panel antenna array having a 17-dBi gain.Every scenario is associated with a transmit power based on its coverage requirements and intersite distance (ISD) [40]: r Rural: the average ISD is 2.5 km and each sector transmits 43 dBm.
r Suburban: the average ISD is 1.1 km and each sector transmits 40 dBm.
r Urban: the average ISD is 0.5 km and each sector transmits 33 dBm.The UE, in turn, features an omnidirectional antenna.The channel from each sector to the UE is modeled as a clustered delay line, customized through the ray tracing package in MatLab 2022b with up to 10 reflections.
As mentioned in Section V, the PRS was introduced for use cases that require accurate and real-time location in 5G-NR.It addresses the two issues of hearability and resource element density as follows: r To increase hearability, allowing the UE to conduct accu- rate ToF measurements from various gNBs at once without interference, PRS multiplexes in frequency the different sequences through a parameter called γ.Specifically, it accommodates γ = 2, 4, 6 or 12 staggered diagonal patterns, which allows an interference-free transmission of up to 12 different PRS sequences.r These patterns occupy resource elements at all subcarriers, so as to handle the high frequency selectivity (long delay spreads) that arise in long-range transmissions [41], and they further occupy multiple symbols in time, to accrue energy against the noise.PRS reaches a maximum bandwidth of 100 MHz, which brings about high ToF estimation accuracy.
Interspersing data symbols within the PRS can degrade the positioning performance [37] and thus such option is not considered here.We configure the PRS with γ equal to the number of simulated gNBs, which ensures no inter-gNB interference in the PRS.There is, however, PRS interference across sectors belonging to the same gNB, and this is included in the signal-tointerference-plus-noise ratio (SINR) calculations since it affects the hearability of each gNB sector at the UE.
In the sequel, for the sake of specificity, one of the most commonly available FR1 channels in Europe is selected (channel n41), whereby the carrier frequency is f c = 2.5 GHz.The maximum PRS bandwidth of 100 MHz is used, with a subcarrier spacing of 30 kHz.ToF measurements are conducted at R 5G-NR = 100 Hz.
ToF Distortion Correction: To model the channel via raytracing, a 3D digital map of each scenario is employed.This allows for a realistic simulation of the signal propagation thus the determination of the corresponding ToF in 3D.Then, to position on the 2D plane, the horizontal projection of the obtained 3D distance estimates is needed.However, the maps do not provide information about the vertical dimensions of the 3D objects, which makes it impossible to know the exact height of the gNBs placed atop the buildings.Hence, an exact projection of the 3D measurements on the horizontal plane is not possible.To sidestep this limitation of Cellmapper, we capitalize on the strong correlation that exists between the 3D distances and their 2D projections.A linear regression [42] is devised using a set of 3D ToF distance measurements and the corresponding exact 2D distances, based on which the height of the gNBs can subsequently be gauged and the dataset of 3D ToF distance measurements D can be corrected onto a new matrix of projected measurements.Although some lingering distortion remains after this correction, it is small relative to the errors induced by effects such as multipath and NLoS.

C. 5GNSS Simulation Environment
From the respective configurations of GNSS and 5G-NR, F = R 5G-NR /R GNSS = 10.For its part, the oversampling factor is set to a = 10, balancing the improvement in accuracy and the increase in latency that growing factors bring about.As far as the weighting is concerned, the L + J weights are initialized to 1 in what we denote fusion full.Then, the following alternatives are entertained based on the data available at the UE: 1) L weights based on the power received from the gNBs and J weights equal to 1. 2) L weights based on the estimated distances to the gNBs and J weights equal to 1. 3) L weights based on HDOP of the gNBs, and J weights based on the HDOP of the satellites.As mentioned in Section III, HDOP is a standard measure of how much the errors in distance estimation alter the position estimation on the horizontal plane [34].One value is calculated for the L gNBs and another value for the J satellites. 4) L weights based on the power received from each gNB multiplied by the corresponding SINR at the UE and the estimated distances, to emphasize the best gNBs, and J weights equal to 1.
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TABLE I SCENARIO CHARACTERISTICS AND CONFIGURABLE PARAMETERS
To contrast these alternatives, 5GNSS is evaluated on the same part of the dataset with each of them.Shown in Fig. 6 is the performance in terms of RMSE, median, and 80% positioning error, from which the 3rd alternative turns out to be the best.This approach weights the measurements from the gNBs and visible satellites with the reciprocal of their HDOPs.
Table I summarizes the parameters selected for the simulations.

VIII. PERFORMANCE EVALUATION
As detailed in Section VI-B, oversampling allows including in the fusion process gNBs that produced a very low number of estimates within the GNSS interval, and that would otherwise be excluded.Consequently, oversampling expands the pool of nodes considered for positioning.Subsequent application of EWMA then smoothens the measurements, sharpening the accuracy of the distance measurements and, by extension, the final position estimation.Furthermore, this establishes a dependency of the final measurement within the window on the entire set of preceding samples.It is this dependency that enables 5GNSS to harness the higher rate of 5G-NR without sacrificing valuable information.
The favorable impact of oversampling and smoothing is depicted in Fig. 7; the processing diminishes the median, 80%, and RMS errors by 23%, 11%, and 12%, respectively as compared to raw measurements.Compared to oversampling alone, the use of EWMA not only reduces outliers in distance estimations by 15%, but also contributes to a general error reduction in the median, 80%, and RMS errors by 18%, 8%, and 7.5%.Finally, we consider taking the median value of the sample window as alternative approach to benchmark our processing strategy.As we can see it becomes apparent that the weighted approach inherent in EWMA facilitates better incorporation of past samples, leading to a reduction in the median, 80%, and RMS errors of 20%, 2% and 5%, respectively, as well as to a 2% reduction in outliers.
Finally, by virtue of the weighting approach set forth in Section VII-C, the fusion is dominated by the more favorable system, GNSS or 5G-NR.In the considered scenarios (urban, suburban, rural), 5G-NR and GNSS follow an inverse trend in terms of number of available nodes: 5G-NR deployments are denser in urban settings, while GNSS satellites are more visible in rural ones.Thus, we expect the advantage of 5GNSS over GNSS to be most pronounced in urban situations.
Next, the performance of 5GNSS in the considered scenarios is illustrated during an initial portion of the ground truth dataset, corresponding to a five minutes drive in the corresponding scenario.
Rural: In this scenario, the UE follows an almost straight trajectory at 56 Km/h on average.Shown in Fig. 8(a) is the GNSS performance, alongside its counterpart for stand-alone systems.Thanks to the clear-sky conditions, GNSS exhibits median, 80%, and RMS errors of 0.61 m, 1 m, and 0.78 m, respectively.Meanwhile, 5G-NR suffers from low availability of gNBs, at best three or four, and long transmission ranges, such that its contribution to 5GNSS is minor.Nonetheless, its inclusion shrinks the median, 80%, and RMS errors down to 0.38 m, 0.61 m, and 0.48 m, respectively.In terms of RMSE, this amounts to a 17% reduction.
Suburban: Here the UE moves at 30 km/h on average, making turns around buildings, but also traveling by a relatively opensky park area.The overall GNSS visibility is lower than in the rural scenario.As per Fig. 8(b), GNSS delivers median, 80%, and RMS errors of 0.6m, 0.92m, and 0.73m, very similar to the rural case.In contrast, 5GNSS reaches 0.5m, 0.61m, and 0.48m, which in terms of RMSE amounts to a 7% reduction.This more modest improvement is explained by the still generous number of visible satellites, which limits the benefits of incorporating 5G-NR.Moreover, the corresponding gNBs are subject to multipath and to a reduced LoS probability.
Urban: Finally, in the urban scenario the UE is moving among high-rise buildings and narrow streets, the typical urban canyons, at 36 km/h on average.The propagation is affected by strong multipath and the probability of LoS is rather low.GNSS suffers from low satellite visibility (a minimum of 6 for 17% of the inference time, a maximum of 9 for 32% of that time).Referring to Fig. 8(c), GNSS shows median, 80%, and RMS errors of 0.96m, 1.63m, and 1.41m.At the same time, stand-alone 5G-NR counters the challenging nature of the propagation environment with a higher density of gNBs, achieving the lower values of 0.54m, 0.84m, and 0.65m.Fusing both, 5GNSS reaches 0.46m, 0.67m, and 0.53m, for reductions in the RMSE sense of 103.5% relative to GNSS and 18% relative to 5G-NR.As expected, in an urban environment GNSS performs worse than in the other scenarios and the contributions from 5G-NR become most relevant.
Stand-alone 4G-LTE and 5G-NR: The higher sampling frequency and broader bandwidth of 5G-NR, together with the new PRS described in Section VII-B, improve also its stand-alone performance.To gauge this improvement, 4G-LTE is considered with the maximum bandwidth of 20 MHz, a subcarrier spacing of 15 kHz, and the PRS as specified by the standard [43].As confirmed by Fig. 8, 5G-NR does outperform 4G-LTE, with RMS error reductions of 51%, 57% and 65% in the rural, suburban and urban scenarios respectively.

IX. SUMMARY
This paper has explored the potential of fusing 5G-NR and GNSS localization systems to improve the accuracy and reliability of current positioning solutions.The performance of the proposed 5GNSS approach has been evaluated in urban, suburban, and rural vehicular scenarios, and results have been provided regarding the impact of the number of gNBs and satellites available, the reductions in the distance estimation error, and the ensuing improvements in positioning accuracy.
In the considered scenarios, and under the assumptions made in the paper, 5GNSS outperforms current GNSS, 4G-LTE, and 5G-NR localization systems with an error reduction ranging between 60% in the rural case to 40% in the urban case (at 80% of the CDF).Moreover, 5GNSS exhibits strong robustness across the different scenarios, with the RMSE always in the vicinity of 0.5m.
Perfect synchronization between GNSS and 5G-NR has been posited in the evaluations.As a part of our future work, a full experimental evaluation of the proposed approach and the baselines is envisioned to further enhance the realism of our simulation-derived benchmarks by accounting for synchronization errors.We anticipate that this assessment will result in generally higher localization errors compared to those documented in this study.Nevertheless, we anticipate the performance improvement of 5GNSS to remain consistent.We thus conclude that future positioning systems requiring high accuracy and robustness, e.g., autonomous driving, will strongly benefit from incorporating 5GNSS-like fusion solutions.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

r
Measurements from gNBs with SNR < SNR min are re- moved.This yields a new set of L gNB measurements that excludes overly noisy values.

Finally
, the UE position is estimated from ζ via multilateration.Let ζ be the vector of true distances between the UE and the L + J nodes.The least-squares problem in (3) becomes δt UE , (x, ŷ) = arg min L +J z=1 ζ z − ζz

Fig. 4 .
Fig. 4. Comparison between real visible satellites of the GNSS and Galileo constellation and the simulated visible satellites, in the three scenarios.(a) Rural.(b) Suburban.(c) Urban.

Fig. 5 .
Fig. 5. Sensitivity analysis of 5GNSS according to the number of available gNBs and visible satellites.

Fig. 7 .
Fig. 7. Effect of oversampling and EWMA on the distance estimation error.

Federico
Campolo received the M.Sc.degree in telecommunications engineering from Politecnico di Milano, Milan, Italy, in 2021, with a thesis on a computer vision algorithm for passive detection, localization and tracking of vulnerable road users.He is currently working toward the Ph.D. degree in telecommunications engineering with University Pompeu Fabra, Barcelona, Spain.He is currently a Researcher with i2CAT Foundation, Barcelona, Spain.His research on wireless localization systems, with a particular interest in 5G-NR positioning for autonomous driving applications.Andra Blaga received the B.Sc. degree in 2022 in telecommunications engineering from the Polytechnic University of Catalonia, Barcelona, Spain, where she is currently working toward the M.Sc.degree in advanced telecommunications engineering.She is also a Junior Researcher with i2CAT Foundation, Barcelona.Her research interests include localization, UAVs, machine learning techniques, and 5G networks with a particular interest in positioning.